Local Reaching Centrality

Local reaching centrality (Mones et al. 2012) measures how much of the network a node reaches. On an unweighted directed network it is the share of the other nodes reachable from the node. On an unweighted undirected network it is the mean inverse distance to the other nodes, harmonic centrality divided by \(n - 1\).

Usage

centrality_reaching_local(x, mode = "all", ...)

Arguments

x: Network input accepted by centrality.
mode: Direction for directed networks: "all" (default), "out" or "in".
...: Further arguments to centrality.

Value

A named numeric vector with one score per node, in input node order.

Details

A network counts as weighted unless every weight is 1, and weighted = FALSE gives the unweighted form. In the weighted form a shortest path uses the edge lengths \(W/w_e\), with \(W\) the total edge weight, and each reached node contributes the mean edge weight along its path; the sum is divided by \(n - 1\). With mode = "out" the weighted values equal networkx.local_reaching_centrality() with normalized = False. mode = "all" treats edges as undirected, and "in" counts the nodes that reach the node. A negative weight raises an error. reaching_global is the network-level hierarchy measure built from these scores.

References

Mones, E., Vicsek, L., & Vicsek, T. (2012). Hierarchy measure for complex networks. PLoS ONE, 7(3), e33799.

Examples

centrality_reaching_local(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#> 0.13055556 0.37277778 0.09703704 0.15333333 0.08703704 0.18851852 0.14333333 
#>   Evaluate     Create      Share 
#> 0.22722222 0.24592593 0.24444444